BMTS415 - IfE

BMTS415
Probability and Probabilistic Models

MQF Level: 6

ECTS Value: 5 ECTS

Self-Study Hours: 60

Duration: 10 Sessions

Contact Hours: 25

Mode of Delivery: Blended

Assessment Hours: 40

Entry Requirements

Applicants applying for the module are to be in possession of the following:

1 An MQF Level 3 (minimum Grade 5 or C) in Maltese, English Language and Mathematics awarded by MATSEC or an equivalent examination body recognised by the IfE

AND

A minimum of one of the following:
a) An awarded MATSEC Certificate or equivalent (MQF Level 4) with a Grade C or better in Mathematics at Advanced Level; OR
b) Three subjects at advanced level (MQF Level 4) including a Grade C or better in Mathematics and another subject, and at least a Grade D in a third subject; OR
c) Two subjects at Advanced Level (MQF Level 4) at Grade C or better including Mathematics, and three intermediate subjects with a minimum Grade D.

Overall Objectives and Outcomes

The unit aims to first introduce the course participants to basic ideas on probability. The unit will then cover different ways of showing a sample space such as Venn Diagrams and Tree Diagrams as well choosing which type of sample space is most suited for a particular situation. This unit shall then focus on distribution functions for Discrete and Continuous Random Variables with particular importance being given to graphical interpretation.

The following Probability Distributions will be discussed:

The Binomial Distribution
The Hypergeometric Distribution
The Poisson Distribution
The Normal Distribution

By the end of this module, the learner will be able to:

Competences

Represent and interpret complex datasets using Venn Diagrams and Tree Diagrams demonstrating a strong grasp of relationships and probabilities within the data;
apply and visualize the Complement and Addition Rules on Venn Diagrams ensuring a comprehensive understanding of probability theory;
Critically evaluate and select the most appropriate measure of Central Tendency based on the nature and distribution of the dataset;
Develop curriculum related material to be used to explain probability in the classroom;
Plan different activities to maximise students’ understanding of probability.

Knowledge

Distinguish between discrete and continuous data;
Distinguish between empirical and theoretical probability;
List the benefits and drawbacks of both empirical and theoretical probability;
Describe the meaning of dependent and independent events;
Identify situations that involve permutations and those that involve combinations;
Describe the meaning of mathematical expectation, variance and standard deviation;
Distinguish between the Binomial, Hypergeometric, Poisson and Normal Distributions.

Skills

Apply the formula for Conditional Probability to solve complex problems, demonstrating an ability to identify and analyse dependent events within various mathematical contexts;
Use the appropriate formulae for permutations and combinations to accurately determine outcomes in both simple and complex scenarios;
Use binomial coefficients in combinations to solve advanced problems illustrating a thorough understanding of their role in probability theory and algebraic expressions;
Interpret and analyse a Venn Diagram and a Tree Diagram to extract data and probabilities;
Work with distribution functions for discrete and continuous random variables applying them to diverse probability models and interpreting their significance in various statistical contexts;
Apply different Probability Distributions selecting and utilising the appropriate distribution model.

Assessment Methods

This module will be assessed through: Class Contribution, Presentation.